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Reversible Conservative Rational Abstract Geometrical Computation Is Turing-Universal

  • Jérôme Durand-Lose
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3988)

Abstract

In Abstract geometrical computation for black hole computation (MCU ’04, LNCS 3354), the author provides a setting based on rational numbers, abstract geometrical computation, with super-Turing capability. In the present paper, we prove the Turing computing capability of reversible conservative abstract geometrical computation. Reversibility allows backtracking as well as saving energy; it corresponds here to the local reversibility of collisions. Conservativeness corresponds to the preservation of another energy measure ensuring that the number of signals remains bounded. We first consider 2-counter automata enhanced with a stack to keep track of the computation. Then we built a simulation by reversible conservative rational signal machines.

Keywords

Abstract geometrical computation Conservativeness Rational numbers Reversibility Turing-computability 2-counter automata 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jérôme Durand-Lose
    • 1
  1. 1.Laboratoire d’Informatique Fondamentale d’OrléansUniversité d’OrléansORLÉANS

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